Post by Daniel Jones
A lot of people confuse turbulent flow with pressure separation. They are two
separate phenomenon. You can have attached flow or separated flow. Separated
flow generally has much more drag. You can also have a laminar or turbulent
boundary layer. A laminar boundary layer generally has less drag but can be
only maintained over slender bodies, like airfoil sections (and then only
sometimes) which unless some sort of active means of boundary layer control
(e.g. suction) is employed. For low drag on a shape that will not sustain
a laminar boundary layer, you want to eliminate separation. As it turns out,
inducing turbulence is a great way to do this. The profile drag of an object
can be spilt into two components:
Cd = Cdf + Cdp
where
Cd = profile drag coefficient
Cdp = pressure drag coefficient due to flow separation
Cdf = skin friction drag coefficient due to surface roughness
in the presence of laminar/turbulent flow
The drag which comprises the Cdf component is caused by shear stress induced
when air molecules collide with the surface of a body. A smooth surface will
have a low Cdf. Also, the Cdf is lower for laminar flow and higher for
turbulent flow. Cdp, on the other hand, is caused by the fore-and-aft pressure
differential created by flow separation. Usually, Cdp is lower for turbulent
flow and higher for laminar flow. In many cases, inducing turbulence will
dramatically decrease the pressure drag component, decreasing the overall drag.
Airplanes use this trick all the time.
Back in the 19th century, when scientists were just beginning to study the
field of aerodynamics, an interesting observation was made with respect to
the drag of a cylinder. Since a cylinder is symmetric front-to-back (and
top-to-bottom), their early theories predicted it should have no drag (or
lift). If you plot the (theoretical) pressure distribution along the
surface of the cylinder (remembering that pressure acts perpendicular to a
surface) and decompose it into horizontal (drag) and vertical (lift)
components, you'll find that the pressure on the front face of the cylinder
(from -90 to +90 degrees) and the pressure on the rear face ( from +90 to
+270 degrees) are equal in magnitude but opposite in direction, exactly
cancelling each other out. Therefore, there should be no drag or lift.
However, if you actually measure the pressure distribution, you'll find
there are considerably lower pressures on the rear face, resulting in
considerable drag. This difference between predicted and observed drag
over a cylinder was particularly bothersome to early aerodynamicists who
termed the phenomenon d'Alembert's paradox. The problem was due to the
fact that the original analysis did not include the effects of skin
friction at the surface of the cylinder. When air flow comes in contact
with a surface, the flow adheres to the surface, altering its dynamics.
Conceptually, aerodynamicists split airflow up into two separate regions,
a region close to the surface where skin friction is important (termed the
boundary layer), and the area outside the boundary layer which is treated
as frictionless. The boundary layer can be further characterized as
either laminar or turbulent. Under laminar conditions, the flow moves
smoothly and follows the general contours of the body. Under turbulent
conditions, the flow becomes chaotic and random.
It turns out that a cylinder is a very high drag shape. At the speeds
we're talking about, a cylinder has a drag coefficient of between 0.4 and
1.17. An efficient shape like a symmetric airfoil (that is aligned
with the airflow, i.e. is at 0 degrees angle of attack) may have a Cd of
0.005 to 0.01. Think about what this means. An airfoil that is 40 to 80
inches tall may have approximately the same drag as a 1 inch diameter
cylinder.
Luckily, there are easy ways of reducing a cylinder's drag. Another thing
the early aerodynamicists noticed was that as you increased the speed of
the air flowing over a cylinder, eventually there was a drastic decrease in
drag. The reason lies in different effects laminar and turbulent boundary
layers have on flow separation. For reasons I won't get into here, laminar
boundary layers separate (detach from the body) much more easily than
turbulent ones. In the case of the cylinder, when the flow is laminar,
the boundary layer separates earlier, resulting in flow that is totally
separated from the rear face and a large wake. As the air flow speed is
increased, the transition from laminar to turbulent takes place on the front
face. The turbulent boundary layer stays attached longer so the separation
point moves rearward, resulting in a smaller wake and lower drag. In the
case of the cylinder, Cd can drop from 0.4 to less than 0.1.
You don't have to rely on high speeds to cause the bondary layer to "trip"
from laminar to turbulent. Small disturbances in the flow path can do the
same thing. A golf ball is a classic example. The dimples on a golf ball
are designed to promote turbulence and thus reduce drag on the ball in
flight. Trip strips are employed on wings for the same reason. If you look
closely, you'll notice that some Indy and F1 helmets have a boundary layer
trip strip to reduce buffeting. It seems odd but promoting turbulence can
reduce buffeting by producing a smaller wake.
Another consequence of skin friction on a cylinder is that you can generate
substantial lift with a spinning cylinder. By spinning a cylinder you can
speed up the flow over the top and slow down flow under the bottom, resulting
in a lift producing pressure differential. In aerodynamics, this is known as
the Magnus effect.
The speed at which a laminar boundary layer becomes turbulent is determined by
the Reynolds number, which is defined as:
Re_x = (Rho * V * X)/Mu
where:
Re_x = Reynolds number at location x (a dimensionless quantity)
Rho = freestream air density
V = freestream flow velocity
x = distance from the leading edge
Mu = freestream viscosity, a physical property of the gas (or liquid)
involved, varies with temperature, at standard conditions mu is
approximately 3.7373x10E-07 slug/(ft*sec) for air.
The location along the body at which the flow transitions from laminar to
turbulent determines the critical Reynolds number. Below this number, the
flow is laminar, above it's turbulent. Since the Reynolds number varies
linearly with the location along the body and with velocity, the faster you
go, the farther forward the transition point moves. At cruising speed on a
typical jet airliner, only a small region near the leading edge may be
laminar. Slow speed gliders with very slender (but still with rounded, blunt,
leading edges) may maintain laminar flow over most of the wing surface but
this is not the case for most practical aircraft. Note that glider wings
are typically designed with very short chord lengths (x distances) to help
promote laminar flow. A laminar boundary layer is desirable when there is no
pressure separation but when there is, a turbulent boundary layer can yield
less drag. Technically speaking, separated flow is not turbulent, even though
it is random and chaotic (and very draggy). Be aware that the laminar and
turbulent concepts apply only to the boundary layer, which may be a few inches
(or less) thick. Beyond the boundary layer, flow is treated as frictionless
(inviscid).
A couple of guys at work (then McDonnell Aircraft, now Boeing), tufted a 1987
Mustang LX from the center of the roof to the taillights. They were trying to
use vortex generators to increase the flow attachment on the rear glass. Vortex
generators are devices which are put in the flow field to intentionally induce
turbulent flow. They are often used on aircraft to re-attach and direct flow
(especially over control surfaces). Their vortex generators were based on
aircraft designs and they used a hang glider airspeed indicator on a pole to
measure the boundary layer thickness across the roof. They made the vortex
generators two inches tall to be conservative (the boundary layer was
approximately one inch thick and a rule of thumb is to make the generators 1.5
time the boundary layer thickness). They didn't see an improvement in coast
down times, but the tufts did appear a little better behaved with the vortex
generators. They believe the turn at the back of the roof may be too sharp to
permit attached flow. They also noted that much of the clean wing flow
appeared to be coming from around the sides of the car.
Dan Jones
